Applicability of a constant Young's modulus in geometrically nonlinear elasticity

Abstract

The aim of this paper is to demonstrate through a simple problem that the use of a constant Young's modulus in numerical analyses of geometrically nonlinear elasticity problems should be considered as a potential source of inaccuracy, depending on what work-conjugate stress and strain measures the formulation uses. Importance of the Biot stresses and Jaumann strains as conjugate engineering stress and strain measures in nonlinear elasticity is emphasized.